Can interactive visualization tools engage and support pre-university students in exploring non-trivial mathematical concepts?

Computers and Education

Volumn 54, Issue 4, 2010, Pages 972-991

  Liang, Hai Ning ^a   Sedig, Kamran ^a  

^a UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

Computer supported mathematics learning; Design of educational software; Human computer interfaces; Interactive visualization tools; Pre university education

Indexed keywords

EDUCATIONAL SOFTWARE; HUMAN COMPUTER INTERFACES; INTERACTIVE VISUALIZATION TOOL; MATHEMATICS LEARNING; UNIVERSITY EDUCATION;

COMPUTER SOFTWARE; DESIGN; HUMAN COMPUTER INTERACTION; INFORMATION SYSTEMS; INTERFACES (COMPUTER); KNOWLEDGE MANAGEMENT; MATHEMATICAL TECHNIQUES; VISUALIZATION;

STUDENTS;

EID: 77249094473     PISSN: 03601315     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compedu.2009.10.001     Document Type: Article

References (66)

1. Ary D., Jacobs L.C., and Razavieh A. Introduction to research in education. 6th ed. (2002), Wadsworth/Thomson Learning, Belmont
2. In: Card S., Mackinlay J.D., and Shneiderman B. (Eds). Readings in information visualization: Using vision to think (1999), Morgan Kaufman, San Francisco, CA
3. Benyon D., Turner P., and Turner S. Designing interactive systems: People, activities, contexts, technologies (2005), Addison-Wesley Longman Ltd, Harlow, England
4. Beynon, B., Nehaniv, C. L., & Dautenhahn, K. (Eds.). (2001). Cognitive technology: Instruments of mind: Proceedings of the 4th international cognitive technology conference (CT 2001), August 6-9, Coventry, UK. New York, NY: Springer-Verlag.
5. Burgoon J.K., Bonito J.A., Bengtsson B., Cederberg C., Lundeberg M., and Allspach L. Interactivity in human-computer interaction: A study of credibility, understanding, and influence. Computers in Human Behavior 16 (2000) 553-574
6. Chen C. Information visualization: Beyond the horizon (2004), Springer-Verlag, London, UK
7. Cheng P. Electrifying diagrams for learning: Principles for complex representational systems. Cognitive Science 26 (2002) 685-736
8. Coxeter H.S.M. Regular complex polytopes. 2nd ed. (1991), Cambridge University Press, Cambridge, UK
9. In: Cuoco A.A., and Curcio F.R. (Eds). The roles of representation in school mathematics: 2001 yearbook (2001), National Council of Teachers of Mathematics, Reston, VA
10. Devlin K. Mathematics, the science of patterns: The search for order in life, mind, and the universe (2003), Scientific American Library, New York, NY
11. Duval, R. (2002). Representation, vision, and visualization: Cognitive functions in mathematical thinking. In Proceedings of Twenty-Fourth annual meeting of the North American chapter of the international group for the psychology of mathematics education 2002, Athens, GA, USA, ERIC Clearinghouse for Science, Mathematics and Environmental Education (pp. 311-335).
12. Elliott, J. & Bruckman, A. (2002). Design of a 3D interactive math learning environment. In Proceedings of the 4th conference on designing interactive systems: Processes, practices, methods, and techniques, London, England (pp. 64-74).
13. Field A. Discovering statistics using SPSS. 2nd ed. (2005), SAGE Publications Ltd, London, UK
14. Field A., and Hole G. How to design and report experiments (2003), SAGE Publications Ltd, London, UK
15. Gadanidis G., Sedig K., and Liang H.-N. Designing online mathematical investigation. Journal of Computers in Mathematics and Science Teaching 23 3 (2004) 275-298
16. In: Glasgow J., Narayanan N.H., and Chandrasekaran B. (Eds). Diagrammatic reasoning: Cognitive and computational perspectives (1995), MIT Press, Cambridge, MA
17. Gregory A., State A., Lin M.C., Manocha D., and Livingston M.A. Interactive surface decomposition for polyhedral morphing. The Visual Computer 15 (1999) 453-470
18. Hanson A.J., Munzner T., and Francis G. Interactive methods for visualizable geometry. IEEE Computer 27 7 (1994) 73-83
19. IMT (2009). Interactive Math Tools: Cabri3D. Accessed February 2009.
20. Jackiw N. The Geometer's Sketchpad, v. 3.0 (1995), Key Curriculum Press, Berkeley, CA
21. In: Jonassen D.H., Beissner K., and Yacci M. (Eds). Structural knowledge: Techniques for representing, conveying, and acquiring structural knowledge (1993), Lawrence Erlbaum Associates, Hillsdale, NJ
22. Jonassen D.H. Modeling with technology: Mindtools for conceptual change. 3rd ed. (2006), Pearson Education, Inc, Upper Saddle River, New Jersey
23. Jonassen D.H., and Carr C.S. Mindtools: Affording multiple knowledge representations for learning. In: Lajoie S.P. (Ed). Computers as cognitive tools: No more walls (2000), Mahwah, NJ, Lawrence Erlbaum Associates pp. 165-196
24. Keller P.R., and Keller M.M. Visual cues: Practical data visualization (1993), IEEE Computer Society Press, Silver Spring, MD
25. Kennedy S. Using video in the BNR usability lab. ACM SIGCHI 21 2 (1989) 92-95
26. Kirsh D. Interactivity and multimedia. Instructional Science 25 (1997) 79-96
27. In: Lajoie S. (Ed). Computers as cognitive tools (2000), Lawrence Erlbaum Associates, Mahwah, NJ
28. Larkin J., and Simon H. Why a diagram is (sometimes) worth ten thousand words. Cognitive Science 11 (1987) 65-99
29. Liang H.-N., and Sedig K. Application of frameworks in the analysis and (re)design of interactive visual learning tools. Journal of Interactive Learning Research 20 2 (2009) 215-254
30. Liang H.-N., and Sedig K. Characterizing navigation in interactive learning environments. Journal of Interactive Learning Environments 17 1 (2009) 53-75
31. Morey J., and Sedig K. Adjusting degree of visual complexity: An interactive approach for exploring four-dimensional polytopes. The Visual Computer: International Journal of Computer Graphics 20 (2004) 1-21
32. National Council of Teachers of Mathematics. NCTM, (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
33. National Council of Teachers of Mathematics. NCTM, (2008a). Standards electronic examples. Accessed May 2008.
34. National Council of Teachers of Mathematics. NCTM, (2008b). Illuminations activities. Accessed May 2008.
35. National Library of Virtual Manipulatives. NLVM (2008). http://nlvm.usu.edu/en/nav/vlibrary.html Accessed July 2008.
36. Paivio A. The empirical case for dual coding. In: Yuille J.C. (Ed). Imagery, memory and cognition (1983), Lawrence Erlbaum Associates, Hillsdale, NJ
37. In: Peterson D. (Ed). Forms of representation (1996), Intellect Books, Exeter, UK
38. Palais R.S. The visualization of mathematics: Towards a mathematical exploratorium. Notices of the American Mathematical Society 46 6 (1999) 647-658
39. Pedagoguery Software (2004). Tess (Version 1.70) [Computer software]. Terrace, B.C., Canada: Pedagoguery Software Inc. Accessed November 2006.
40. Pettersson R. Visuals for information research and practice (1989), Educational Technology Publications, Englewood Cliffs, NJ
41. Pettersson R. Message design. In: Plomp T., and Ely D.P. (Eds). International encyclopedia of educational technology. 2nd ed. (1996), Elsevier Science Ltd, Oxford, UK
42. Preece J., Rogers Y., and Sharp H. Interaction design: Beyond human computer interaction (2002), John Wiley and Sons Inc, New York, NY
43. Richter-Gebert, J. & Kortenkamp, U. H. (1999). Cinderella - The interactive geometry software. London: Springer. Accessed June 2008.
44. Rowhani S., and Sedig K. E-books plus: Role of interactive visuals in exploration of mathematical information and e-learning. Journal of Computers in Mathematics and Science Teaching 24 3 (2005) 273-298 Norfolk, VA: AACE
45. Scaife M., and Rogers Y. External cognition, innovative technologies, and effective learning. In: Gardenfors P., and Johansson P. (Eds). Cognition, education, and communication technology (2005), LEA pp. 181-202
46. Scharein, R. G. (2006). KnotPlot [Computer software]. Vancouver, Canada: Hypnagogic Software. Accessed November 2006).
47. Sedig K., Klawe M., and Westrom M. Role of interface manipulation style and scaffolding on cognition and concept learning in learnware. ACM Transactions on Computer-Human Interaction 1 8 (2001) 34-59
48. Sedig K., and Liang H.-N. Interactivity of visual mathematical representations: Factors affecting learning and cognitive processes. Journal of Interactive Learning Research 17 2 (2006) 179-212
49. Sedig K., Rowhani S., and Liang H.-N. Designing interfaces that support formation of cognitive maps of transitional processes: An empirical study. Interacting with Computers: The Interdisciplinary Journal of Human-Computer Interaction 17 4 (2005) 419-452
50. Sedig K., Rowhani S., Morey J., and Liang H.-N. Application of information visualization techniques to the design of a mathematical mindtool: A usability study. Information Visualization 2 (2003) 1142-1159
51. Sedig K., and Sumner M. Characterizing interaction with visual mathematical representations. International Journal of Computers for Mathematical Learning 11 1 (2006) 1-55
52. Sinclair N., Zazkis R., and Liljedahl P. Number worlds: Visual and experimental access to elementary number theory concepts. International Journal of Computers for Mathematical Learning 8 3 (2003) 235-263
53. Spence R. Information visualization: Design for interaction. 2nd ed. (2007), Pearson Education Limited, Harlow, UK
54. Stochastic-Lab (2006). Archim (Version 1.1). Accessed July 2008.
55. Thomas, J. J. & Cook, K. A. (2005). Illuminating the path: The research and development agenda for visual analytics. National Visualization and Analytics Center.
56. TMF (2008). The Math Forum Library. Accessed July 2008.
57. Tufte E.R. Envisioning information (1990), Graphics Press, Cheshire
58. Tufte E.R. Visual explanations: Images and quantities, evidences and narratives (1997), Graphics Press, Cheshire
59. VMM (2008). Virtual Math Museum. Accessed July 2008.
60. Ware C. Information visualization: Perception for design. 2nd ed. (2004), Morgan Kaufmann Publishers, San Francisco, CA
61. Webb R. Stella: Polyhedron navigator. Symmetry: Culture and Science 11 1-4 (2003) 231-268
62. Weeks, J. (2005). KaleidoTile (Version 3.0) [Computer Software]. Accessed July 2008.
63. West T.G. Forward into the past: A revival of old visual talents with computer visualization. ACM SIGGRAGPH Computer Graphics 29 4 (1995) 14-19
64. Wilkinson L. The grammar of graphics (1999), Springer-Verlag, Berlin
65. Zhang J. The nature of external representations in problem solving. Cognitive Science 21 2 (1997) 179-217
66. Zimmermann, W. & Cunningham, S. (Eds., 1991). Visualization in teaching and learning mathematics. Mathematical Association of America.